Rafael Nadal

Sixth seed Nadal, bidding for a men's record 21st Grand Slam title, beat Germany's Hanfmann 6-2 6-3 6-4.

Hanfmann saved four match points, including two on the Spaniard's serve, before the 2009 champion secured victory on Rod Laver Arena.

Alexander Zverev also reached the third round after beating Australia's John Millman in straight sets.

Despite a spirited performance from the Australian, the German third seed won 6-4 6-4 6-0 to set up a meeting with Moldovan qualifier Radu Albot, who beat wildcard Aleksandar Vukic 6-4 7-6 (7-4) 6-4.

Nadal has spent the last four months on the sidelines with a foot injury while he also struggled with back issues at the start of the year.

The 35-year-old Spaniard was knocked out at Roland Garros in the semi-finals before he was forced to pull out of Wimbledon, the Tokyo Olympics and the U.S. Open. He last competed in August at the Citi Open in Washington.

"I am feeling better, if not I will not be here. That's the goal, I know the comeback will not be easy," Nadal told reporters.

Nadal, a two-time champion at the All England Club, announced via a series of social media posts on Friday that he would also miss the Tokyo Olympics to rest and recover “after listening to my body.”

“The goal,” the 35-year-old Spaniard said, “is to prolong my career and continue to do what makes me happy.”

Osaka’s agent, Stuart Duguid, wrote in an email that the four-time Grand Slam champion does plan to head to the Summer Games after skipping Wimbledon.

Nadal, bidding for a record-extending 14th French Open title, won the first five games of the match as he looked on course to repeat his drubbing of the Serb in last year's final.

But world number one Djokovic seized the momentum, winning the second set and then edging a pulsating 97-minute third set on a tiebreak, having saved a set point.

The soccer-style atmosphere created by a crowd of around 5,000 inside Court Philippe Chatrier reached a crescendo towards the end of the third as the Paris COVID-19 curfew loomed.

The Spaniard was in danger of being thrashed when Rublev led by a break in the second set, having dominated the opener, but showed his trademark grit to battle back.

Rublev was unrelenting, however, and bludgeoned his way into a 5-1 lead in the second set after breaking the Nadal serve three times. Nadal held serve but the 23-year-old world number eight then finished it off with a crushing forehand winner.

It was Rublev's first win against Nadal and the first time he had managed to win a set.

Barty overcame a stumbling start to claim a 6-2 6-4 victory over Ekaterina Alexandrova at an empty Margaret Court Arena on Saturday.

The 24-year-old would have expected the backing of a fiercely partisan crowd for a weekend evening match at her home Grand Slam, but Melbourne's five-day lockdown left her playing in front of officials, ballkids and coaches.

While most other players have seen plenty of empty courts on the WTA tour over the last year, it was a new experience for Barty, who elected to stay home while the COVID-19 pandemic raged around the world.

Medvedev's first career victory over the 20-times Grand Slam champion sent him through to a final showdown against Dominic Thiem who earlier beat Novak Djokovic in another titanic clash.

The 24-year-old Medvedev reached the semi-finals as the only player to post a 100% record in his group, including a superb defeat of Djokovic.

Thiem will attempt to go one better than last year when he lost to Stefanos Tsitsipas in the final.

Nadal, who reached the final at Bercy once in 2007, was only briefly in the mix, conceding serve three times.

Zverev will look to claim his fourth Masters title against Russian third seed Daniil Medvedev, who qualified with a commanding 6-4 7-6(4) victory against Canadian Milos Raonic.

Meanwhile Novak Djokovic has sealed the year-end men's world number one tennis ranking for the sixth time to go level with childhood hero Pete Sampras after closest rival Nadal opted against playing in the ATP Tour event in Sofia next week.

With his record-improving 13th triumph at Roland Garros, world number two Nadal is now tied with Swiss Roger Federer as the player with the most men's singles major titles.

Nadal was the early aggressor as he choked Djokovic to win the opening set in brutal fashion having made only two unforced errors. He then kept a firm grip on a subdued Djokovic in the second set under the roof of court Philippe Chatrier.

The Spaniard, chasing a record-extending 13th triumph at Roland Garros, will meet the world number one for the seventh time at Roland Garros, having beaten him six times out of seven, including twice in the two finals they played.

The 34-year-old Nadal, now undefeated in 13 French Open semi-finals, once again relied on his massive forehand to notch up his 10th win in 11 encounters with Schwartzman, who beat him at the Italian Open last month.